def product_2103

bendtorch-core@0.1.0.0 · src/tensor/axis_algebra.bend:1559

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend as Axis

1559def product_2103(+dims: List<&2, Nat>, length: {List.length(&2, Nat, dims) == 4n : Nat}) -> {Shape.numel(Axis.order(Nat, dims, [2n, 1n, 0n, 3n])) == Shape.numel(dims) : Nat}:
1560  match dims:
1561    case Nil{}:
1562      Empty.absurd({Shape.numel(Axis.order(Nat, Nil{}, [2n, 1n, 0n, 3n])) == Shape.numel(Nil{}) : Nat}, nat_clash(0n, 4n, length, {==}))
1563    case +x0 <> Nil{}:
1564      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> Nil{}, [2n, 1n, 0n, 3n])) == Shape.numel(x0 <> Nil{}) : Nat}, nat_clash(1n, 4n, length, {==}))
1565    case +x0 <> +x1 <> Nil{}:
1566      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> Nil{}, [2n, 1n, 0n, 3n])) == Shape.numel(x0 <> x1 <> Nil{}) : Nat}, nat_clash(2n, 4n, length, {==}))
1567    case +x0 <> +x1 <> +x2 <> Nil{}:
1568      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> Nil{}, [2n, 1n, 0n, 3n])) == Shape.numel(x0 <> x1 <> x2 <> Nil{}) : Nat}, nat_clash(3n, 4n, length, {==}))
1569    case +x0 <> +x1 <> +x2 <> +x3 <> Nil{}:
1570      Equal.trans(Nat, Nat.mul(x2, Nat.mul(x1, Nat.mul(x0, Nat.mul(x3, 1n)))), Nat.mul(x2, Nat.mul(x0, Nat.mul(x1, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Equal.cong(Nat, Nat, value => Nat.mul(x2, value), Nat.mul(x1, Nat.mul(x0, Nat.mul(x3, 1n))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x3, 1n))), mul_swap(x1, x0, Nat.mul(x3, 1n))), Equal.trans(Nat, Nat.mul(x2, Nat.mul(x0, Nat.mul(x1, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), mul_swap(x2, x0, Nat.mul(x1, Nat.mul(x3, 1n))), Equal.trans(Nat, Nat.mul(x0, Nat.mul(x2, Nat.mul(x1, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Nat.mul(x0, Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n)))), Equal.cong(Nat, Nat, value => Nat.mul(x0, value), Nat.mul(x2, Nat.mul(x1, Nat.mul(x3, 1n))), Nat.mul(x1, Nat.mul(x2, Nat.mul(x3, 1n))), mul_swap(x2, x1, Nat.mul(x3, 1n))), {==})))
1571    case +x0 <> +x1 <> +x2 <> +x3 <> +x4 <> +tail:
1572      Empty.absurd({Shape.numel(Axis.order(Nat, x0 <> x1 <> x2 <> x3 <> x4 <> tail, [2n, 1n, 0n, 3n])) == Shape.numel(x0 <> x1 <> x2 <> x3 <> x4 <> tail) : Nat}, nat_clash(5n+List.length(&2, Nat, tail), 4n, length, {==}))